COMMERCIAL AND INDUSTRIAL MATHEMATICS

The Quantitative Finance Seminar has been a centerpiece of the
Commercial/Industrial program at the Fields Institute since 1995.
Its mandate is to arrange talks on current research in quantitative
finance that will be of interest to those who work on the border
of industry and academia. Wide participation has been the norm with
representation from mathematics, statistics, computer science, economics,
econometrics, finance and operations research. Topics have included
derivatives valuation, credit risk, insurance and portfolio optimization.
Talks occur on the last Wednesday of every month throughout the
academic year and start at 5 pm. Each seminar is organized around
a single theme with two 45-minute talks and a half hour reception.
There is no cost to attend these seminars and everyone is welcome.

To be informed of speakers and titles for upcoming seminars and
financial mathematics activities, please subscribe to the Fields
mail list.

Seminars 2009-10

June 2, 2010
5 p.m.

Freddy Delbaen (ETH Zurich)BSDE and time consistencyAbstract: the capital requirements for financial institutions
should satisfy rules that encourage diversification, avoid
risk concentration and take into account the time aspect of
uncertainty. They also should allow to allocate, in a consistent
way, the risk capital to the different branches of the financial
institution. This is best done via convex, time consistent
risk measures, a mathematical concept that is based on the
theory of stochastic processes, backward stochastic differential
equations and semi-linear PDE.

H. Mete Soner, Department of Mathematics, ETH ZurichFinancial markets with uncertain volatility.
Even in simple models in which the volatility is only known
to stay in two bounds, it is quite hard to price and hedge
derivatives which are not Markovian. The main reason for this
difficulty emanates from the fact that the relevant set of
probability measures is not dominated by one measure. In this
talk we will prove a martingale representation theorem for
this market. This result provides a complete answer to the
questions of hedging and pricing. The main tools are the theory
of nonlinear G-ex pectati ic analysis of Denis & Martini
and the second order backward stochastic differential equations.
This is joint work with Nizar Touzi from Ecole Polytechnique
and Jianfeng Zhang from University of Southern California.

Past Seminars

September 30, 2009

Ulrich Horst, Humboldt University BerlinHidden Liquidity and the Optimal Placement of Iceberg Orders
Audio and
Slides of the TalkAlmost all electronic trading systems are based on Limit
Order Books (LOBs) in which all unexecuted limit orders are
stored while awaiting execution. Not all the available liquidity
is openly displayed, though. Most exchanges offer liquidity
providers the option of shielding all or portions of their
limit orders from public display. These modified order types,
known as hidden orders or iceberg orders, meet the demands
of traders who perceive benefits in obscuring their immediate
trading needs from other market practitioners. We propose
a simple mathematical model of a LOB within which to study
the problem of the optimal display size of limit orders placed
in the spread or at the top of the book. One of the most important
determinants of the optimal display size is the amount of
hidden liquidity with higher time priority of the hidden part
of the submitted order. We estimated this quantity using recent
NASDAQ data. Our empirical analysis shows that the spread
together with the visible volume at the top of the book often
well predicts the amount of hidden liquidity in the spread
and on top of the book. We also report a couple of other empirical
findings including the dependence of hidden liquidity on average
daily trading volumes and average quote sizes, and the distribution
of hidden liquidity in the spread.

The talk is based on joint work with Gökhan Cebiroglu
(Humboldt University) and Mark DiBattista (Deutsche Bank AG)
&Jeremy Graveline, University of MinnesotaG10 Swap and Exchange RatesAudio
and Slides of the TalkIn this talk we show how to extend single-currency dynamic
term structure models to a multi-currency setting. When the
risk-neutral pricing measures, or risk premia, are denominated
in two different currencies they must differ by the covariance
of the exchange with the other factors in the model. As an
illustrative example, we provide estimates for a Gaussian
model of the term structure of swap rates and exchange rates
in the G10 countries. There are 9 exchange rates and each
yield curve is described by 2 or 3 factors, for a total of
37 factors in the model. The parameters that govern the covariances
and risk-neutral drifts are relatively easy to estimate. However,
it is much harder to reliably estimate the risk premia parameters
that relate the risk-neutral and statistical measures. We
examine the performance of models for 7 years out-of-sample
and show that models with a small number of priced risk factors
provide a good in-sample fit and the best out-of-sample results.
This talk discusses joint work with Scott Joslin at MIT.

October 28, 2009

Tomasz R Bielecki,
Illinois Institute of Technology Counterparty Credit Risk: CVA computation under netting
and collateralization(There is no audio recording of this
talk)
We first present a general model for counterparty risk. We give
are presentation formula for the Credit Value Adjustment (CVA)
accounting for netting and collateralization in the context
of bilateral counterparty risk. Then, we specify the results
to the case of counterparty credit risk, where we consider a
credit risky portfolio between two default prone counterparties.
The underlying model for the dependence between defaults is
based on the concept of Markov copula. Some numerical results
illustrating computation of relevant quantities (such as CVA,
EPE) will be presented.

Tom Hurd, McMaster UniversityCredit Risk via First Passage for Time Changed Brownian
MotionsAudio and slides of
TalkThe first passage structural approach to credit risk,
while very natural, is beset by technical difficulties that
make it
inflexible in practice. Time changed Brownian motions (TCBMs)
offer a simple but mathematically interesting way to circumvent
these technicalities and open the door to a number of innovations.
After a quick sketch of the basic properties of TCBM models,
I show that they can give an excellent fit to the dynamics
of credit default swaps
observed in the market. I then consider a more complex ``hybrid''
framework that can model the joint dynamics of equity and
credit derivatives. Finally, I will touch briefly on how the
TCBM framework extends to multiple firms, paving the way for
a consistent ``bottom up'' approach to portfolio credit derivatives.
This is a talk aimed at people who really work with credit
default swaps and other credit risky securities, and their
feedback will be welcomed!

November 25, 2009

Frank Milne, Queen's
UniversityApproaches for Modeling Liquidity and Systemic RisksAudio and slides
of Talk
The paper outlines some basic approaches to modeling liquidity,
and its implications for asset pricing and portfolio strategy.
These idea can be used to model a Risk Management system with
liquidity problems. In addition they can be extended to explore
Systemic Risks.

Traian Pirvu, McMaster UniversityTime Consistency in Portfolio ManagementAudio and slides
of Talk
There are at least two examples in portfolio management that
are time inconsistent. 1) Maximizing utility of intertemporal
consumption and final wealth assuming a hyperbolic discount
rate (the discount rate increases with time). 2) Mean-variance
utility: This case is a continuous time version of the standard
Markowitz investment problem, and the time inconsistencies
are due to the wealth's variance (which is nonlinear and depends
on the starting wealth). In this talk I will focus on the
first example. There is strong evidence that individuals discount
future utilities at nonconstant rates. The notion of optimality
then disappears, because of time inconsistency and rational
behaviour then centers around equilibrium strategies. I will
investigate portfolio management with hyperbolic discounting,
and I will show that this may explain some well known puzzles
of portfolio management. This is joint work with Ivar Ekeland.

January
20, 20104:30 -5:15 p.m.
**note time

Eckhard Platen,
University of Technology , Sydney Real World Pricing of Long Term ContractsAudio and slides
of Talk
Long dated contingent claims are relevant in insurance, pension
fund management and derivative pricing. This paper proposes
a paradigm shift in the valuation of long term contracts, away
from classical no-arbitrage pricing towards pricing under the
real world probability measure. In contrast to risk neutral
pricing, the long term excess return of the equity market, known
as the equity premium, is taken into account. Further, instead
of the savings account, the numeraire portfolio is used, as
the fundamental unit of value in the analysis. The numeraire
portfolio is the strictly positive, tradable portfolio that
when used as benchmark makes all benchmarked nonnegative portfolios
supermartingales, which means intuitively that these are in
the long run downward trending or at least trendless. Furthermore,
the benchmarked real world price of a benchmarked claim is defined
to be its real world conditional expectation. This yields the
minimal possible price for its hedgable part and minimizes the
variance of the benchmarked hedge error. The pooled total benchmarked
replication error of a large insurance company or bank essentially
vanishes due to diversification. Interestingly, in long term
liability and asset valuation, real world pricing can lead to
significantly lower prices than suggested by classical no-arbitrage
arguments. Moreover, since the existence of some equivalent
risk neutral probability measure is no longer required, a wider
and more realistic modeling framework is available for exploration.
Classical actuarial and risk neutral pricing emerge as special
cases of real world pricing.

Note Feb. 24 revised
speaker, Tobias Adrian will not be speaking at this time

February 24, 2010
5 pm.

Raphael Douady, Riskdata
The StressVaR: a New Risk Concept for Superior Fund Allocation
Joint work with Cyril Coste and Ilija I. Zovko Audio and slides
of Talk

In this paper we introduce a novel approach to risk estimation
based on nonlinear factor models - the "StressVaR"
(SVaR). Developed to evaluate the risk of hedge funds, the
SVaR appears to be applicable to a wide range of investments.
The computation of the StressVaR is a 3 step procedure whose
main components we describe in relative detail. Its principle
is to use the fairly short and sparse history of the hedge
fund returns to identify relevant risk factors amonga very
broad set of possible risk sources. This risk profile is obtained
by calibrating a collection of nonlinear single-factor models
as opposed to a single multi-factor model. We then use the
risk profile and the very long and rich history of the factors
to asses the possible impact of known past crises on the funds,
unveiling their hidden risks and so called "black swans".In
backtests using data of 1060 hedge funds we demonstrate that
the SVaR has better or comparable properties than several
common VaR measures - shows less VaR exceptions and, perhaps
even more importantly, in case of an exception, by smaller
amounts.The ultimate test of the StressVaR however, is in
its usage as a fund allocating tool. By simulating a realistic
investment in a portfolio of hedge funds, we show that the
portfolio constructed using the StressVaR on average outperforms
both the market and theportiolios constructed using common
VaR measures.For the period from Feb. 2003 to June 2009, the
StressVaR constructed portfolio outperforms the market by
about 6% annually, and on average the competing VaR measures
by around 3%.The performance numbers from Aug. 2007 to June
2009 are even more impressive. The SVaR portfolio outperforms
the market by 20%, and the best competing measure by 4%.

March 31, 2010
5 pm.

Dilip Madan (University of Maryland)Capital Requirements, Acceptable Risks and the Value of
the Taxpayer Put

Limited liability for the firm in the presence of unbounded
liabilities delivers a free put option to the firm that is
rarely valued and accounted for. We christen this put option
the taxpayer put. In addition the optimality of free markets
is called into question by the introduction of adverse risk
incentives exaggerated by compensation aligned to stock market
values. In such a context we introduce the concept of socially
acceptable risks, operationalized by a positive expectation
after distortion of the distribution function for risky cash
flows. This results in a definition of capital requirements
making the risks undertaken acceptable to the wider community.
Enforcing such capital requirements can mitigate the perverse
risk incentives introduced by limited liability provided that
the set of acceptable risks is suitably conservatively defined.
Additionally the value of the free taxpayer put may be substantially
reduced. We illustrate all computations for the six major
US banks at the end of 2008.

From mathematical perspective, risk management is a procedure
for shaping a risk distribution. Popular functions for managing
risk are Value at-Risk (VaR) and Conditional Value-at-Risk
(CVaR). Reasons affecting the choice between VaR and CVaR
are based on the differences in mathematical properties, stability
of statistical estimation, simplicity of optimization procedures,
acceptance by regulators, etc. We explain strong and weak
features of these risk measures and illustrate them with examples.
We demonstrate several risk management/optimization case studies
conducted with Portfolio Safeguard decision support software.
In particular, we will discuss how to calibrate risk preferences
of investors doing risk management with options.

Bio:Professor Stan Uryasev is director of the Risk Management
and Financial Engineering Lab and director of the PhD Program
with Concentration in Quantitative Finance at the University
of Florida. His research is focused on efficient computer
modeling and optimization techniques and their applications
in finance and military projects. He published three books
(monograph and two edited volumes) and about eighty research
papers. He is a co-inventor of the Conditional Value-at-Risk
and the Conditional Drawdown-at-Risk optimization methodologies.
He is the founder of American Optimal Decisions (AORDA.com)
developing optimization software in risk management area:
VaR, CVaR, Default Probability, Drawdown, Credit Risk minimization.

Stan Uryasev is a frequent speaker at academic and professional
conferences. He has delivered seminars on the topics of risk
management and stochastic optimization. He is on the editorial
board of a number of research journals and is Editor Emeritus
and Chairman of the Editorial Board of the Journal of Risk.

- Benefits and limitations of rational models of asset pricing
- A alternative framework for asset price dynamics based on
investor behavior
- Price-following and herding effects and their impact on
the distribution of asset prices
- Fat tail effects. The impact of market feedback, credit
cycles, crises and uncertainty
- Quantifying the risk of extreme events. From theory to practice.

Summary
A predominant view in the literature of market behavior is
that investors are driven by rationality -that is, investors
are presumed to make logical and sensible decisions all the
time. Evidence accumulated over years, and in particular during
turbulent times, has shown consistently that investors are
far less rational in their decision making that the theory
assumes. Understanding investors' behavior is important for
developing more realistic models of asset price dynamics capable
of capturing the extreme changes in prices observed during
periods of market booms and crashes.

In the presentation I will elaborate on an asset pricing
model based on market behavior and uncertainty. The phenomenological
model of asset valuation dynamics includes investor behavior
patterns based on price momentum and trends. The model produces
fat-tail distributions of asset prices remarkably similar
to the observed distributions, and provides a simple framework
for understanding the potential divergence between fundamental
and market valuations under uncertainty.

***Please note that the second talk
by Igor Halperin has been canceled due to unforseen circumstances.